The Affine Particle-In-Cell Method

Abstract:
Hybrid Lagrangian/Eulerian simulation is commonplace in computer
graphics for fluids and other materials undergoing large deformation.
In these methods, particles are used to resolve transport
and topological change, while a background Eulerian grid is used
for computing mechanical forces and collision responses. Particlein-Cell
(PIC) techniques, particularly the Fluid Implicit Particle
(FLIP) variants have become the norm in computer graphics calculations.
While these approaches have proven very powerful, they
do suffer from some well known limitations. The original PIC is
stable, but highly dissipative, while FLIP, designed to remove this
dissipation, is more noisy and at times, unstable. We present a novel
technique designed to retain the stability of the original PIC, without
suffering from the noise and instability of FLIP. Our primary
observation is that the dissipation in the original PIC results from
a loss of information when transferring between grid and particle
representations. We prevent this loss of information by augmenting
each particle with a locally affine, rather than locally constant, description
of the velocity. We show that this not only stably removes
the dissipation of PIC, but that it also allows for exact conservation
of angular momentum across the transfers between particles and
grid.